Quasi-static Locomotion Research Articles

Reuleaux Triangle–Based Two Degrees of Freedom Bipedal Robot

This paper presents the design, modeling, analysis, and experimental results of a novel bipedal robotic system that utilizes two interconnected single degree-of-freedom (DOF) leg mechanisms to produce stable forward locomotion and steering. The single DOF leg is actuated via a Reuleaux triangle cam-follower mechanism to produce a constant body height foot trajectory. Kinematic analysis and dimension selection of the Reuleaux triangle mechanism is conducted first to generate the desired step height and step length. Leg sequencing is then designed to allow the robot to maintain a constant body height and forward walking velocity. Dynamic simulations and experiments are conducted to evaluate the walking and steering performance. The results show that the robot is able to control its body orientation, maintain a constant body height, and achieve quasi-static locomotion stability.

Interaction Between Inertia, Viscosity, and Elasticity in Soft Robotic Actuator With Fluidic Network

Soft robotics is an emerging bioinspired concept of actuation, with promising applications for robotic locomotion and manipulation. Focusing on actuation by pressurized embedded fluidic networks, existing works examine quasi-static locomotion by inviscid fluids. This paper presents analytic formulation and closed-form solutions of an elastic actuator with pressurized fluidic networks, while accounting for the effects of solid inertia and elasticity, as well as fluid viscosity. This allows modeling the system's step response and frequency response as well as suggesting mode elimination and isolation techniques. The theoretical results describing the viscous–elastic–inertial dynamics of the actuator are illustrated by experiments. The approach presented in this paper may pave the way for the design and implementation of soft robotic legged locomotion that exploits dynamic effects.

High-slope terrain locomotion for torque-controlled quadruped robots

Research into legged robotics is primarily motivated by the prospects of building machines that are able to navigate in challenging and complex environments that are predominantly non-flat. In this context, control of contact forces is fundamental to ensure stable contacts and equilibrium of the robot. In this paper we propose a planning/control framework for quasi-static walking of quadrupedal robots, implemented for a demanding application in which regulation of ground reaction forces is crucial. Experimental results demonstrate that our 75-kg quadruped robot is able to walk inside two high-slope ($$50^\circ $$50ź) V-shaped walls; an achievement that to the authors' best knowledge has never been presented before. The robot distributes its weight among the stance legs so as to optimize user-defined criteria. We compute joint torques that result in no foot slippage, fulfillment of the unilateral constraints of the contact forces and minimization of the actuators effort. The presented study is an experimental validation of the effectiveness and robustness of QP-based force distributions methods for quasi-static locomotion on challenging terrain.

Design and Quasi-Static Locomotion Analysis of the Rolling Disk Biped Hybrid Robot

Motivated by the need for greater speed, efficiency, and adaptability in climbing and walking robots, we have developed a bipedal planar robot that complements its walking and climbing capabilities with rolling. Rolling capabilities are provided by an innovative morphology, without the need for additional resources beyond those required by walking and climbing. Herein, we present the design of this robot, the development of a quasi-static rolling controller, and a comparison of experimentally obtained speed and energy data for walking versus rolling locomotion. We show that rolling can significantly improve energy efficiency over walking-as much as a factor of 5.5. We also demonstrate the ability to roll up slopes and roll over obstacles.

A General Stance Stability Test Based on Stratified Morse Theory With Application to Quasi-Static Locomotion Planning

This paper considers the stability of an object supported by several frictionless contacts in a potential field such as gravity. The bodies supporting the object induce a partition of the object's configuration space into strata corresponding to different contact arrangements. Stance stability becomes a geometric problem of determining whether the object's configuration is a local minimum of its potential energy function on the stratified configuration space. We use stratified Morse theory to develop a generic stance stability test that has the following characteristics. For a small number of contacts - less than three in 2D and less than six in 3D - stance stability depends both on surface normals and surface curvature at the contacts. Moreover, lower curvature at the contacts leads to better stability. For a larger number of contacts, stance stability depends only on surface normals at the contacts. The stance stability test is applied to quasi-static locomotion planning in two dimensions. The region of stable center-of-mass positions associated with a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -contact stance is characterized. Then, a quasi-static locomotion scheme for a three-legged robot over a piecewise linear terrain is described. Finally, friction is shown to provide robustness and enhanced stability for the frictionless locomotion plan. A full maneuver simulation illustrates the locomotion scheme.

Computation and Graphical Characterization of Robust Multiple-Contact Postures in Two-Dimensional Gravitational Environments

This paper is concerned with computation and graphical characterization of robust equilibrium postures suited to quasistatic multi-legged locomotion. Quasistatic locomotion consists of postures in which the mechanism supports itself against gravity while moving its free limbs to new positions. A posture is robust if the contacts can passively support the mechanism against gravity as well as disturbance forces generated by its moving limbs. This paper is concerned with planar mechanisms supported by frictional contacts in two-dimensional gravitational environments. The kinematic structure of the mechanism is lumped into a rigid body B having the same contacts with the environment and a variable center of mass. Inertial forces generated by moving parts of the mechanism are lumped into a neighborhood of wrenches centered at the nominal gravitational wrench. The robust equilibrium postures associated with a given set of contacts become the center-of-mass locations of B that maintain equilibrium with respect to all wrenches in the given neighborhood. The paper formulates the computation of the robust center-of-mass locations as a linear programming problem. It provides graphical characterization of the robust center-of-mass locations, and gives a geometric algorithm for computing these center-of-mass locations. The paper reports experiments validating the equilibrium criterion on a two-legged prototype. Finally, it describes initial progress toward computation of robust equilibrium postures in three dimensions.

Equilibrium analysis of multi-limbs walking and climbing robots

The paper discusses the complex problem of assessing online the static equilibrium of statically-indeterminate climbing and walking robots (CLAWARs) with quasi-static locomotion. The method proposed is general and works for whatever number of legs and ropes operated by actuated winches connecting the robot to the environment. The configuration of the robot is assigned. First, the compliance of the robot body, of the legs and the compliances of the ground and the ropes are modeled as localized elasticities. The static equilibrium problem of the resulting model is statically-determinate under the hypothesis that the foot and rope points (where the ropes are fixed to the robot body) are joined to the ground by bilateral constraints. Since these constraints are unilateral (the feet are contact points and can detach from the ground, and the ropes can become slack), it is necessary to apply an iterative solving procedure in order to solve the static equilibrium problem. The method presented in the paper is a fast and effective alternative to nonlinear analysis of a finite element model of the robot at any assigned configuration. As an example, we consider the case of the heavy-duty CLAWAR Roboclimber.

Multi-legged multi-roped walking and climbing robots: online static equilibrium analysis

The paper proposes a fast method to solve the equilibrium problem of statically indeterminate walking and climbing robots with quasi-static locomotion and whatever number of legs and ropes connecting the robot frame to the ground. The configuration is instantaneously assigned. Legs and rope winches are imagined blocked. Due to the number of legs and ropes, the robot is a statically indeterminate system under unilateral constraints: in order to solve the system of the equilibrium equations, it is necessary to take into account the compliance of the robot and of the terrain. This can be done by non-linear analysis of a finite element model of the robot, including the ground characteristics, but this is very time consuming. The method presented in the paper seems an effective alternative. To assess its performances, the method is applied to the heavy-duty climbing robot Roboclimber with satisfactory results. The running time is low enough to allow the application for the online gait planning and for real-time control of the robot. The method will be soon used as decision support for online gait planning within the remote control system of Roboclimber.